Clarke was fined 20 per cent of his match fee on Monday after a nasty and foul-mouthed exchange with Anderson during the last throes of Australia's 381-run victory in Brisbane.
But television commentator Warne, who has access to uncensored versions of stump microphone recordings, claims Anderson threatened debutant George Bailey, who was fielding at bat-pad.
"@MClarke23 stuck up for his debutant Bailey as he should have too as capt after Anderson said he wanted to punch Bailey in the face.
"Unfortunately only Clarke's reaction to Anderson's was heard live, we (commentators) all heard Anderson's sledge that led to Clarke reacting.
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"To me it should just stay out in the middle. They all shook hands had a giggle & moved on. By fining Clarke it's made a big deal out of it.
"Everyone should have just laughed, moved on & be thankful for ashes fever. Bring on Adelaide I'm sure both teams are saying #ashes.
"Lastly as an international sportsman, if you decide to dish it out ie sledging you have to be prepared to cop it back too & not complain."
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Bailey heeded Warne's advice about leaving disagreements between players on the field when he spoke to reporters after arriving home in Hobart.
"(Anderson) must have been just a bit upset about the way the game was going I guess," Bailey said.
"I'm not one for saying much. I'm pretty quiet out there."